You have found the following ages (in years) of 4 snakes. Those snakes were randomly selected from the 44 snakes at your local zoo: $ 12,\enspace 5,\enspace 5,\enspace 16$ Based on your sample, what is the average age of the snakes? What is the standard deviation? You may round your answers to the nearest tenth.
Solution: Because we only have data for a small sample of the 44 snakes, we are only able to estimate the population mean and standard deviation by finding the sample mean $({\overline{x}})$ and sample standard deviation $({s})$ To find the sample mean , add up the values of all $4$ samples and divide by $4$ $ {\overline{x}} = \dfrac{\sum\limits_{i=1}^{{n}} x_i}{{n}} = \dfrac{\sum\limits_{i=1}^{{4}} x_i}{{4}} $ $ {\overline{x}} = \dfrac{12 + 5 + 5 + 16}{{4}} = {9.5\text{ years old}} $ Find the squared deviations from the mean for each sample. Since we don't know the population mean, estimate the mean by using the sample mean we just calculated {6.25} + {20.25} + {20.25} + {42.25}} {{4 - 1}} $ {s^2} = \dfrac{{89}}{{3}} = {29.67\text{ years}^2} $ As you might guess from the notation, the sample standard deviation $({s})$ is found by taking the square root of the sample variance $({s^2})$ ${s} = \sqrt{{s^2}}$ $ {s} = \sqrt{{29.67\text{ years}^2}} = {5.4\text{ years}} $ We can estimate that the average snake at the zoo is 9.5 years old. There is also a standard deviation of 5.4 years.